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Pencil (DS) Problem

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by Nikhil Tayade » Fri Dec 25, 2009 9:41 am
Hi, Can you please help me out with this problem & let me know the answer.

Marta bought several Pencils, If Each pencil was either a 23-cent pencil or a 21-cent pencil, How many 23-cent pencils did Marta buy?

1) Marta bought a total of 6 pencils
2) Total value of pencils Marta bought was 130 cents

A. Statement 1 alone is sufficient to solve
B. Statement 2 alone is sufficient to solve
C. Both statements together are sufficient, but niether statement alone is sufficient to solve
D. Each statement alone is sufficient to solve
E. Statement 1 & 2 together are NOT sufficient to solve this.


Guys I tried to solve this & got the answer. However the logical answer that I got is not matching with the answer in the GMAT tets prep Software. Kindly let me know your answer & also explaination to some extent if possible

Thanks in Anticipation,
Nikhil
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by papgust » Fri Dec 25, 2009 9:55 am
IMO it is B

Statement I is clearly insufficient.

Statement II: 21x + 23y = 130 [Where x and y are no. of 21-cent pencils and 23-cent pencils respectively]

The best way to approach now is list all the multiples of 21 and 23 and see which combination adds upto 130.

21: 21, 42, 63, 84, 105, 126...
23: 23, 46, 69, 92, 115, 138...

By seeing the only combination that adds up to 130 is (84, 46). 84 is in 4th fourth place of 21 and 46 is in second place of 21. Since we are asked no. of 23-cent pencils, 2 is the answer. Sufficient.


Note: Please post the DS problems in the relevant folder (Data sufficiency)
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by Nikhil Tayade » Fri Dec 25, 2009 10:03 am
Hi, thanks that is the right answer.

I will move this to DS forum. Just as a side note. I thought the answer for this as C (Both statements are together required) Because 23X + 21Y = 320 would be one
& X + Y = 6 would be the equation 2 is what I thought.
And we would need to solve these 2 eqs simultaneously to get the answer.

Anyways thanks a lot buddy
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by viidyasagar » Fri Dec 25, 2009 10:05 am
Let the no of 23 cent pencils be x and the no of 21 cent pencils be y

statement 1 says....x+y = 6.....this doesn't tell me anything

Hence option A and option D are out..we are left with B,C and E

statement 2 says.....23x+21y=130

This is where it gets tricky.........

I am forced to think that this statement alone also doesn't tell me anything...but taken together, i have 2 equations and 2 unknowns hence "C" is the answer.....

But no of pencils must be an integer and since only one combination gives me 130 (as papgust rightly pointed out).....the answer is undoubtedly "B"

tx
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